Transient Electromagnetic Field of an Electric Line Source above a Plane Drude Model Plasmonic Half-space

Abstract

The enhancement of the electromagnetic fleld at the surface of a Drude metal is classifled as the so called surface plasmon efiect. This surface plasmon efiect in a classical Drude model has been investigated extensively in the frequency domain. However, to understand what is actually happening to the electromagnetic fleld at the near vicinity of a Drude metal a thorough analysis in the space-time domain is needed. Once the space-time domain counterpart of the surface plasmon efiect is found, one is able to describe and classify the physical phenomena that are playing a role in the occurrence of this efiect. The phenomenon of surface plasmon resonance of metallic structures has been known and theoret- ically described for more than flfty years. Nowadays, the plasmonic nanostructures are used in a variety of applications, such as molecular sensing and imaging devices, optical devices and meta- materials. One of the materials in which plasmonic efiects are encountered are metals that have a frequency dependant conductivity described by the Drude model. Many researchers investigated Drude model metals in the frequency domain in order to determine the optical behaviour of metals within a certain frequency range. However, to understand what phenomena are at work when the electromagnetic fleld interacts in the near vicinity with a Drude model metal, a thorough analysis in the space-time domain is needed. Once the space-time domain counterpart of the surface plasmon efiect is identifled, a description and classiflcation of the physical phenomena that occur can be given. These results can be of great importance in the fleld of time-domain terahertz spectroscopy. The pulsed electromagnetic radiation from a line source above a plane plasmonic half-space, modeled by a classical Drude model, is investigated. In order to obtain closed-form expressions for the re∞ected electric fleld anywhere above the plasmonic half-space, the re∞ection factor RE that corresponds to the Drude metal half-space is mathematically written in the form of a Laplace transform integral, enabling the application of the Cagniard-de Hoop method. In the Cagniard-de Hoop method the Laplace transform with respect to time is used, in which the Laplace parameter s is kept real and positive in order to ensure causality in the space-time domain expressions for the electromagnetic fleld. Attention is paid to investigate which parts of the Laplace transform integral representation of RE give rise to the surface-plasmon efiect by means of enhancement of the re∞ected electromagnetic fleld at the near vicinity of the Drude metal interface. The derived space-time domain expressions for the re∞ected electric fleld explicitly show the special time and space dependence that exists in the re∞ection factor at the interface of the plasmonic half-space. Consequently, leading to a better understanding of the physical efiects, that occur at the interface of classical Drude metals in the space-time domain. Finally, a suitable source signature is proposed, which enables, without loss of generality, a suitable determination of analytical closed-form inverse Laplace transforms of the distinct source functions. Numerical results that support the conclusions made in this paper will be presented at the Symposium. 2. DESCRIPTION OF THE CONFIGURATION